2.8 is missing the Carve option in the Boolean Modifier
As mentioned here, by developer Sergey Sharybin, 'Carve' was removed in favour of focusing on one boolean implementation (BMesh):


  We've got quite comprehensive BMesh based implementation, which is way
  easier for maintenance than abandoned Carve library.
  
  After all the time BMesh implementation was working on the same level
  of limitations about manifold meshes and touching edges than Carve. Is
  better to focus on maintaining one boolean implementation now.


A task remains open to track any issues with the BMesh implementation:

https://developer.blender.org/T47030

There is also a fairly brief discussion on devtalk.blender.org regarding this topic (there may be other discussions - I just found this link quickly) which includes a few comments from a developer who is working on the BMesh library:

https://devtalk.blender.org/t/carve-was-the-only-boolean-mode-that-worked-for-sculpting-and-it-got-removed-in-2-8-wtf/5576